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1.8.2. “Binary” algorithm

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This algorithm also uses the only one IE (k = 1) and is implemented in the n steps; at the same time, the initial segment AB is divided into the 2n equal parts, i.e., in this case, the (n, 1)-exactness of the algorithm is determined by the following efficiency function:


Note that this algorithm “generates” the binary representation of integers (the “binary system”), which underlies the modern information technology:


where is the bit and 2i(i = 0, 1, 2, …, n – 1) is the weight of the ith digit.

Thus, the above classic measurement algorithms (counting algorithm and “binary” algorithm), on the one hand, generate elementary theory of numbers (counting algorithm) and on the other hand, are the basis of modern computer science (“binary” algorithm).

Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science

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